![]() ![]() ![]() Consequently, LSTM or GRU models with few state variables are necessarily very small (see Supplementary Text), which limits their representational power. ![]() However, these transition functions are inherently shallow ( 7). Typical recurrent networks rely on long short-term memory (LSTM) or gated recurrent unit (GRU) architectures ( 5, 6) to mitigate these problems through gated transition functions (see Table 1). The training of RNNs is notoriously difficult ( 4). At each time step, an input function preprocesses the current inputs, a transition function updates the memory units, and an output function converts the memory units into observable outputs ( 3). RNNs function incrementally and feature memory units, which naturally serve as state variables in the context of material modeling, making them uniquely suited to this problem ( 2). Conceptually, recurrent neural networks (RNNs) ( 1) could alleviate this issue by delivering a universal material model, capable of modeling any material through a simple change of parameters. New classes of materials often require the development of new classes of models with a custom state-space representation (see Fig. Consequently, its formulation is highly specialized. This vector describes succinctly the evolution of the material’s microstructure over time. F Īside from finding the mapping f, a major challenge rests in the choice of the size and contents of the state variable vector χ. ![]()
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